He was awarded the First Prize as flautist and the Conductors Diploma at the Conservatoire Nationale de Paris.

During three years he studied conducting in Munich.

Graf won the First Prize at the International Music Contest of the ARD in Munich and the Bablock Prize of the H. Cohen International Music Award in London.

The multi-talented musician was appointed the youngest principal flutist at the Winterthur Symphony Orchestra and at the Lucerne Festival Orchestra with additional conducting responsibilities.

It followed a period of full time opera and symphonic conducting.

At the age of 21 Graf's recording of the Ibert Flute Concerto earned him immediate and overwhelming international recognition. Since then he made concert tours internationally as well as numerous recordings, television- and radio-recordings and is a regular guest at international music festivals.

He has been a professor at the Basle Music Academy since 1973 and gives master classes internationally.

Graf is also the author of three didactic monographs (see Publications).

From the Academy of Music Cracow he receives the title doctor honoris causa.

From the USA National Flute Association Graf receives the Lifetime Achievement Award 2005.

From the Italian FALAUT-Association he receives the Premio alla Carriera Flauto d’Oro